A particle is performing S.H.M. about x = 0, | vedclass

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(D) The velocity $v$ of a particle performing $S.H.M.$ at a position $x$ is given by the formula: $v = \omega \sqrt{a^2 - x^2}$.Here, $\omega$ is the

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$\frac{4\sqrt{2}\pi a}{3T}$

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(D) The velocity $v$ of a particle performing $S.H.M.$ at a position $x$ is given by the formula: $v = \omega \sqrt{a^2 - x^2}$.Here, $\omega$ is the angular frequency, which is related to the time period $T$ by $\omega = \frac{2\pi}{T}$.Given $x = \frac{a}{3}$, we substitute this into the velocity formula:$v = \left(\frac{2\pi}{T}\right) \sqrt{a^2 - \left(\frac{a}{3}\right)^2}$$v = \left(\frac{2\pi}{T}\right) \sqrt{a^2 - \frac{a^2}{9}}$$v = \left(\frac{2\pi}{T}\right) \sqrt{\frac{8a^2}{9}}$$v = \left(\frac{2\pi}{T}\right) \left(\frac{2\sqrt{2}a}{3}\right)$$v = \frac{4\sqrt{2}\pi a}{3T}$.

$A$ particle is performing $S.H.M.$ about $x = 0$, with an amplitude $a$ and time period $T$. The speed of the particle at $x = \frac{a}{3}$ will be

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